This calculator estimates the elastic buckling (collapse) pressure under uniform external pressure using ideal thin-shell expressions.
Use a mean radius R, thickness t, Young’s modulus E, and Poisson’s ratio ν.
The allowable pressure is computed as p_allow = p_cr / SF, where SF is your safety factor.
- Select a shell model that matches your geometry (cylinder or sphere).
- Enter E and ν for the material, using appropriate units.
- Enter the mean radius and thickness. Keep t < R.
- Optionally enter the length to report ratios like L/t.
- Set a safety factor and choose the output pressure unit.
- Press Calculate to show results above the form.
- Use Download CSV or Download PDF to export results.
| Case | Model | E | ν | R | t | SF | Estimated pcr (MPa) | Estimated pallow (MPa) |
|---|---|---|---|---|---|---|---|---|
| 1 | Long cylinder | 200 GPa | 0.30 | 250 mm | 6 mm | 2.0 | 0.760 | 0.380 |
| 2 | Long cylinder | 69 GPa | 0.33 | 150 mm | 4 mm | 2.5 | 0.367 | 0.147 |
| 3 | Sphere | 200 GPa | 0.30 | 500 mm | 5 mm | 2.0 | 24.209 | 12.105 |
- Imperfections matter: real shells can buckle far below ideal theory.
- Boundary conditions matter: ends, stiffeners, and supports change collapse.
- Use standards for design: apply the relevant pressure-vessel or pipeline code.
- Check units carefully: E and geometry must be consistent.
1) What external pressure buckling means
External pressure places a shell in compression. Thin shells can suddenly form lobes and lose stiffness before material yielding becomes important. This calculator gives an elastic buckling estimate for ideal cylinders and spheres, then computes an allowable pressure using your safety factor.
2) Common engineering situations
Typical cases include vacuum vessels, submarine pipelines, jacketed tanks, and exchanger shells. Buckling can govern when diameter is large, the wall is thin, or the part is imperfect. Designers often evaluate collapse at the maximum external differential pressure, such as full vacuum inside with ambient water or air outside.
3) Inputs that dominate the result
Young’s modulus E scales the critical pressure directly, while Poisson’s ratio ν modifies stiffness through (1 − ν²). Geometry dominates: for long cylinders the ideal relation is proportional to (t/R)³, so a 10% thickness increase raises the estimate by roughly 33%. For spheres the dependence is (t/R)².
4) Understanding the ratios t/R, L/t, and L/R
The ratio t/R summarizes thinness; small values are more buckling-sensitive. The optional ratios L/t and L/R provide context for end effects: short, strongly constrained ends may raise collapse, while flexible boundaries may reduce it. Treat these as indicators, not hard limits.
5) Cylinder versus sphere behavior
Spheres are usually more stable because curvature exists in two directions. Cylinders can buckle into multiple circumferential lobes, and real-world ovality can reduce practical collapse pressure. Use the geometry option that best matches your component.
6) Safety factor and allowable pressure
The tool reports pallow = pcr/SF. Safety factor selection depends on uncertainty in loads, tolerances, corrosion allowance, and inspection level. If you enter an applied pressure, utilization and margin are reported to support fast iterations. For typical thin shells, results can span from a few kPa to multiple MPa, depending mainly on t/R.
7) Practical factors not captured by ideal theory
Real shells have imperfections, weld mismatch, thickness variation, and residual stress. Stiffeners and supports can change the buckling mode, and even small ovality can reduce collapse pressure noticeably. Elastic theory is best used as a screening baseline before standard-based checks, testing, or nonlinear analysis.
8) Next steps for design-quality verification
For critical equipment, confirm boundary conditions and follow the applicable standard. Verify properties at service temperature, include corrosion or wear allowances, and consider knockdown factors for imperfections. When collapse risk is high, use calibrated analysis supported by test evidence.
1) Is this calculator suitable for code compliance?
No. It is an elastic screening estimate for ideal shells. For compliance, use the governing vessel or pipeline standard, including tolerances and external pressure methods.
2) Why does thickness affect results so strongly?
For long cylinders the ideal relation includes (t/R)³, so small thickness changes create large shifts in predicted critical pressure. Buckling stiffness rises quickly as thickness increases.
3) What radius should I enter?
Use the mean (mid-surface) radius for thin shells. If you only know outside diameter, subtract half the thickness to estimate the mean radius.
4) How should I choose the safety factor?
Select a factor that reflects uncertainty in loads, geometry, corrosion, and inspection. Higher uncertainty or severe consequences generally require a larger factor aligned with your design practice.
5) What does utilization greater than 1 mean?
Applied external pressure exceeds the calculated allowable pressure. Reduce the load, increase thickness, reduce radius, add stiffening, or switch to a standard-based method or advanced analysis.
6) Does length change the computed pressure?
Here, length is used to report L/t and L/R for context. In reality, end constraints and shell length can influence buckling modes, especially for short cylinders.
7) Why might real buckling occur below the estimate?
Ovality, dents, weld mismatch, and thickness variation reduce collapse strength. Boundary flexibility and non-uniform pressure can also lower resistance; standards often apply knockdown factors.